Table REF  displays the Shannon entropy as a function of the nuclear charge
\(Z=1,2, \dots , 10\)  for \(d=2, 3, 4\)  and 5 (see also Figure REF ). Two important
features appear in the behavior of the Shannon entropy: \(i\) ) for each fixed value of \(d\) , \(S^{(d)}_{r}\) 
is a strictly decreasing function of \(Z\)  and, \(ii\) ) in agreement with the results for the \(d\) -dimensional
hydrogen atom [1]}, \(S^{(d)}_{r}\)  is a strictly increasing function of \(d\) .
Column 4 of Table REF  shows the results of the Shannon entropy for \(d=3\)  calculated in
[2]} (with 444 basis functions) and [3]} (with a three-parameter wave function). For
\(Z=2, 3\)  the relative error is \(\sim 3\%\)  and for \(Z=4, \dots ,10\)  the relative error decreases from
\(\sim 10\%\)  to \(\sim 0.4\%\)
<TABLE>